In the last three of the chapters in the James Tenney anthology From Scratch: Writings in Music Theory, the author continues to wrestle with the nature of harmony and the perception of pitch. What is interesting is how each of Tenney’s essays on these matters tries to approach the subject from a different point of view, meaning that, by the end of the collection, one is reminded of the problems that three blind men have in trying to describe an elephant. “The Several Dimensions of Pitch,” written in 1993 and revised in 2003, tried to grab this particular elephant by its physiology, beginning with several informative pages that take a deep dive into what is happening in the inner ear. Of greatest interest is the explanation of the difference between hearing a simultaneity of individual tones and hearing them as a single unified stimulus, suggesting that, from an ontological point of view, a “chord” resides in a different category than a single tone.
In itself this is a rather profound insight. The problem is that Tenney does not quite seem to know where to take it. Part of the problem has to do with the fact that he never really reconciles the difference between the mathematical precision of integer ratio with the “fudge factors” of tolerance that arise when listening to real instruments playing their tones. As a result, I come away from Tenney’s speculations reminded of the old joke that the mathematical constant π, a transcendental irrational number, is equal to the integer 3 for very large values of 3.
The following chapter, “On ‘Crystal Growth’ in Harmonic Space,” also written in 1993 and revised in 2003, is the most problematic in the collection. It serves up an abundance of diagrams that get progressively larger and perhaps may be interpreted as a metaphor for crystal growth. For the life of me, I could not make heads or tails out of how to read those diagrams or what Tenney intended them to signify. It is as if he was in search of yet another metaphor to elaborate his thoughts, but it is almost immediately clear that his knowledge of auditory physiology was on much sounder ground than anything involving crystal growth.
The final chapter discusses Tenney’s composition “Diapason” and can be taken, without too much of a stretch, as a summing-up of the entire volume. The composition was clearly intended to make concrete many of Tenney’s abstract speculations on how the concept of harmony could “evolve” to accommodate new concepts of consonance and dissonance in the atonal repertoire. The “punch line” of those speculations is as follows:
Before harmony can evolve, the role of music itself must evolve. Otherwise we will simply be replaying an earlier scenario with minor, “cosmetic” changes in the details.
My own feeling is that there is too much to music to be crammed into a single context, let alone a “role” associated with that context. For my part, I would prefer to fall back on the “definition” that I think was attributed to Erik Satie by John Cage, which declares simply that music is what happens at concerts. I have now lived long enough to see the nature of the concert evolve in any number of imaginative ways, each with its own sense of context. Has music “evolved” along with the concert experience? From the Satie-Cage point of view, I suppose it has!
In the final paragraph of this chapter, Tenney turns his attention to the concept of form, which he declares should be treated “simply as another object of perception.” This takes me back to my own frequently-explored turf of the nature of mind as hypothesized by Gerald Edelman based on speculations by Friedrich Hayek. This involves the principle of “perceptual categorization,” which I discussed when writing about the “META Meta + Hodos” chapter in From Scratch. As I see it, what Tenney calls an “object of perception” is basically what Edelman calls a “perceptual category;” and, on the basis of what Edelman has written about the relationship between brain and perceptual categories, I am not yet convinced that the concept of form is one of those perceptual categories.